K14n12891

Knot presentations

Dowker-Thistlethwaite code

4 10 20 -16 12 2 22 26 -6 24 8 28 18 14

Notes on presentations of K14n12891

Polynomial invariants

Jones polynomial	Data:K14n12891/Jones Polynomial
Alexander polynomial	$t^{4}-8t^{3}+30t^{2}-68t+91-68t^{-1}+30t^{-2}-8t^{-3}+t^{-4}$
Conway polynomial	Data:K14n12891/Conway Polynomial
Determinant	Data:K14n12891/Determinant
Signature	Data:K14n12891/Signature
HOMFLY-PT polynomial	$z^{8}-2a^{2}z^{6}-2z^{6}a^{-2}+4z^{6}+a^{4}z^{4}-6a^{2}z^{4}-3z^{4}a^{-2}+z^{4}a^{-4}+9z^{4}+2a^{4}z^{2}-9a^{2}z^{2}-z^{2}a^{-2}-2z^{2}a^{-4}+6z^{2}+2a^{4}-3a^{2}+2a^{-2}-2a^{-4}+a^{-6}+1$
Kauffman polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 z^{12} $Failed^{-1} +2 z^{12}+7 \text{QuantumGroups$\grave{ }$a} z^{11}+12 z^{11} $Failed^{-1} +5 z^{11} $Failed^{-1} +12 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+10 z^{10} $Failed^{-1} +4 z^{10} $Failed^{-1} +18 z^{10}+13 \text{QuantumGroups$\grave{ }$a}^3 z^9+8 \text{QuantumGroups$\grave{ }$a} z^9-11 z^9 $Failed^{-1} -5 z^9 $Failed^{-1} +z^9 $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^4 z^8-12 \text{QuantumGroups$\grave{ }$a}^2 z^8-16 z^8 $Failed^{-1} -z^8 $Failed^{-1} -36 z^8+4 \text{QuantumGroups$\grave{ }$a}^5 z^7-24 \text{QuantumGroups$\grave{ }$a}^3 z^7-40 \text{QuantumGroups$\grave{ }$a} z^7-5 z^7 $Failed^{-1} +14 z^7 $Failed^{-1} +7 z^7 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^6-17 \text{QuantumGroups$\grave{ }$a}^4 z^6-10 \text{QuantumGroups$\grave{ }$a}^2 z^6-3 z^6 $Failed^{-1} -3 z^6 $Failed^{-1} +3 z^6 $Failed^{-1} +11 z^6-7 \text{QuantumGroups$\grave{ }$a}^5 z^5+20 \text{QuantumGroups$\grave{ }$a}^3 z^5+41 \text{QuantumGroups$\grave{ }$a} z^5-8 z^5 $Failed^{-1} -40 z^5 $Failed^{-1} -18 z^5 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^6 z^4+13 \text{QuantumGroups$\grave{ }$a}^4 z^4+25 \text{QuantumGroups$\grave{ }$a}^2 z^4+2 z^4 $Failed^{-1} -10 z^4 $Failed^{-1} -6 z^4 $Failed^{-1} +16 z^4+3 \text{QuantumGroups$\grave{ }$a}^5 z^3-11 \text{QuantumGroups$\grave{ }$a}^3 z^3-12 \text{QuantumGroups$\grave{ }$a} z^3+21 z^3 $Failed^{-1} +30 z^3 $Failed^{-1} +11 z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^2-7 \text{QuantumGroups$\grave{ }$a}^4 z^2-17 \text{QuantumGroups$\grave{ }$a}^2 z^2+6 z^2 $Failed^{-1} +9 z^2 $Failed^{-1} +4 z^2 $Failed^{-1} -8 z^2+2 \text{QuantumGroups$\grave{ }$a}^3 z-\text{QuantumGroups$\grave{ }$a} z-7 z $Failed^{-1} -7 z $Failed^{-1} -3 z $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^4+3 \text{QuantumGroups$\grave{ }$a}^2-2 $Failed^{-1} -2 $Failed^{-1} - $Failed^{-1} +1}

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